A metric characterization of Riemannian submersions

被引：41

作者：

Berestovskii, VN

Guijarro, L

机构：

[1] Omsk State Univ, Dept Math, Omsk 644077, Russia

[2] Univ Autonoma Madrid, Dept Math, E-28049 Madrid, Spain

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2000年 / 18卷 / 06期

关键词：

metric fibration; Riemannian submersion; submetry;

D O I：

10.1023/A:1006683922481

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A map between metric spaces is called a submetry if it maps balls of radius R around a point onto balls of the same radius around the image point. We show that when the domain and target spaces are complete Riemannian manifolds, submetries correspond to C-1,(1) Riemannian submersions. We also study some consequences of this fact, and introduce the notion of submetries with a soul.

引用

页码：577 / 588

页数：12

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